Sr Examen

Expresión abc∨ab¬c∨a¬bc∨¬abc∨¬ab¬c

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

    Ha introducido [src]
    (a∧b∧c)∨(a∧b∧(¬c))∨(a∧c∧(¬b))∨(b∧c∧(¬a))∨(b∧(¬a)∧(¬c))
    $$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \left(b \wedge \neg a \wedge \neg c\right)$$
    Solución detallada
    $$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \left(b \wedge \neg a \wedge \neg c\right) = b \vee \left(a \wedge c\right)$$
    Simplificación [src]
    $$b \vee \left(a \wedge c\right)$$
    b∨(a∧c)
    Tabla de verdad
    +---+---+---+--------+
    | a | b | c | result |
    +===+===+===+========+
    | 0 | 0 | 0 | 0      |
    +---+---+---+--------+
    | 0 | 0 | 1 | 0      |
    +---+---+---+--------+
    | 0 | 1 | 0 | 1      |
    +---+---+---+--------+
    | 0 | 1 | 1 | 1      |
    +---+---+---+--------+
    | 1 | 0 | 0 | 0      |
    +---+---+---+--------+
    | 1 | 0 | 1 | 1      |
    +---+---+---+--------+
    | 1 | 1 | 0 | 1      |
    +---+---+---+--------+
    | 1 | 1 | 1 | 1      |
    +---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$b \vee \left(a \wedge c\right)$$
    b∨(a∧c)
    FNCD [src]
    $$\left(a \vee b\right) \wedge \left(b \vee c\right)$$
    (a∨b)∧(b∨c)
    FNC [src]
    $$\left(a \vee b\right) \wedge \left(b \vee c\right)$$
    (a∨b)∧(b∨c)
    FNDP [src]
    $$b \vee \left(a \wedge c\right)$$
    b∨(a∧c)